Question: $J$ $K$ $L$ If: $ KL = 2x + 9$, $ JL = 49$, and $ JK = 7x + 4$, Find $KL$.
From the diagram, we can see that the total length of ${JL}$ is the sum of ${JK}$ and ${KL}$ $ {JK} + {KL} = {JL}$ Substitute in the expressions that were given for each length: $ {7x + 4} + {2x + 9} = {49}$ Combine like terms: $ 9x + 13 = {49}$ Subtract $13$ from both sides: $ 9x = 36$ Divide both sides by $9$ to find $x$ $ x = 4$ Substitute $4$ for $x$ in the expression that was given for $KL$ $ KL = 2({4}) + 9$ Simplify: $ {KL = 8 + 9}$ Simplify to find ${KL}$ : $ {KL = 17}$